C₁₇×#13435 #16871179

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13435

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,29)(20,30,34,52)(21,35,39,64)(22,40,43,27)(23,44,45,28)(25,41,48,32)(26,49,51,38)(31,56,36,65)(33,60,61,55)(37,68,70,63)(42,53,74,72)(46,76,78,81)(47,59,75,73)(50,69,71,79)(54,67,80,58)(57,77,66,62);(18,20,24,34)(19,25,29,48)(21,36,39,31)(22,41,43,32)(23,33,45,61)(26,46,51,78)(27,52,40,30)(28,47,44,75)(35,62,64,77)(37,57,70,66)(38,58,49,67)(42,73,74,59)(50,80,71,54)(53,60,72,55)(56,68,65,63)(69,76,79,81);(18,21,22,37,24,39,43,70)(19,26,27,50,29,51,40,71)(20,31,32,57,34,36,41,66)(23,38,42,69,45,49,74,79)(25,46,30,54,48,78,52,80)(28,35,53,63,44,64,72,68)(33,58,59,81,61,67,73,76)(47,77,55,56,75,62,60,65)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6423);